Bus bunching (also referred to as clumping, clustering, or platooning) describes the tendency of buses along a particular transit route to pair or bunch together despite being scheduled to appear at constant intervals. If buses are scheduled to run a certain headway time apart, passengers arriving to a station should not expect to wait more than the headway time for the next bus to arrive. If passengers arrive at a random time, the average waiting time is a half of the headway time. If two buses pair, passengers may wait as long as two headways. If more than two buses bunch up, the wait can be even longer.
These unfavorable outcomes are familiar to regular bus riders. Studies of bus systems reveal that they are prone to instability and bunching. This is at least partially due to the undesired feedback loop between bus headways and the time it takes to load passengers at each station. If a bus falls behind schedule, more passengers tend to accumulate than if it were running the scheduled time ahead of it. Increased passenger accumulation requires the laggard bus to wait even longer at each station, further retarding its progress. Conversely, buses ahead of schedule tend to pick up fewer passengers and can go even further ahead of schedule. The result is bus bunching.
Bus bunching or clustering is discussed in several references, such as U.S. Pat. No. 3,772,691, U.S. Pat. No. 5,739,774, U.S. Pat. No. 6,006,159, U.S. Pat. No. 6,374,176 and US Patent Publication 2010/0299177, all of which are incorporated herein by reference in their entireties.
Conventional ways to control bus bunching involve the insertion of a fixed slack time into the schedule at certain points along the route. This slack artificially delays buses and the passengers on board. This conventional technique has limited effectiveness in reducing bus bunching, while bus operators must use more buses to cover the same route, adding operating cost. Furthermore, passengers in the transit must wait longer at each station as the slack time is absorbed. The slack technique is not adaptive to severe disruptions in which the amount of slack is insufficient and thus bunching can still occur.